The potential energy for a conservative system is given by:
$U = ax^2 - bx$
Where $a$ and $b$ are positive constants. The law of the force governing the system is:

Is the work done by non-conservative forces always negative? Discuss.

In the case of non-conservative forces,the following statement is correct.

When a conservative force does positive work on a body,

Which one of the following forces cannot be expressed in terms of potential energy?

Given below are two statements:
Statement $I$: An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $\vec{F}$. The work done by the force is $W = -\int_{r_{1}}^{r_{2}} \vec{F} \cdot d\vec{r}$.
Statement $II$: Any object moving from one location to another location can follow an infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of the above statements, choose the correct answer from the options given below: